Recent content by Accretion

Homework Statement Prove that the product of two consecutive natural numbers is even. 2. The attempt at a solution Hi, I'm just starting to work with proofs by induction, I'm just wondering if this is a valid technique, and/or if I am being too verbose in my proof, thanks! Let...

I'm just factoring the d^{2} out of d^{2}+\frac{\pi d^{2}}{4}. Multiply d^{2}(1+\frac{\pi}{4}) out using the distributive property and you'll get back to d^{2}+\frac{\pi d^{2}}{4}.

I'm not sure I follow your simplification to: A(d)=\frac{\pi d^{2}}{2} My Reasoning: Area of square: d^{2} Area of circle: \pi r^{2} Radius of circle: r=\frac{d}{2} A(d)=d^{2}+\pi r^{2} A(d)=d^{2}+\pi(\frac{d}{2})^{2} A(d)=d^{2}+\frac{\pi d^{2}}{4} A(d)=d^{2}(1+\frac{\pi}{4})

For part a I got A(d)=d^{2}+\frac{\pi d^{2}}{4}=d^{2}(1+\frac{\pi}{4}) I hope I'm understanding the problem correctly, d is also the diameter of the semi-circle on either side, so r=\frac{d}{2}. I think you are neglecting to add the area of the square inbetween those two semi-circles in your...

When you are normally factoring an expression, say x^3+2x^2+x, you factor the largest factor of each term out of the expression, in this case, the x, or x^1 (same thing): x(x^2+2x+1). Can apply that same logic to the case when the exponent is negative, fractional, or both? Hint: What is the...

To put it into greater perspective, Breivik kills 77 people, and gets 21 years. In the US, if you screw up and fail to inform a cop that you are recording an interview, the maximum sentence in some states can be 21 years. While I realize these two cases are in different countries, it just...

menco, take this equation for example: \int x^2 = \frac{x^3}{3} + C, do you remember why we put +C there?